Markov Chain Monte Carlo profile likelihood

We develop a simple and efficient method to approximate profile likelihood functions in directed graphical models based on posterior samples produced using Markov Chain Monte Carlo methods. Specification of prior distributions only have an influence on the definition area of the likelihood approximation, and no further influence on the approximations. The method has been demonstrated on serveral examples with realistic complexity, and the method looks promising. The method can be viewed as a supplement to a Bayesian analysis with the aim of doing prior sensitivity analysis.